Tuesday, 3 December 2013

Regional PIOMAS Volume Data

I've been busy recently getting the code I use to handle the PIOMAS gridded data into a more tidy state, it was getting the situation where I, the author, was having trouble remembering where the heck I'd coded what. As part of this I've finally dealt with the issue of making a matching set of PIOMAS data broken down into the same regions Cryosphere Today uses. I have also improved the grid box area calculation with help from Dr Zhang.

Regions have been calculated by using the Cryosphere Today graphic of regions as a template, this is actually an NSIDC 25km Polar Stereographic mask (thanks to Wipneus for that hint). The template has been converted to an array in memory with region codes replacing colours, some errant pixels have been cleaned up manually with the array loaded into a spreadsheet. 'Coast' pixels have been assigned the nearest sea region number, should it be needed PIOMAS gridded data has its own land mask. The template has been used as a look up table and each PIOMAS grid box assigned its closest region number. Some manual editing has then been done, mainly due to differences between the NSIDC and PIOMAS land masks in the Canadian Arctic Archipelago.

For those who are using the gridded data the binary region mask is available here, it matches the flat format of the heff files but is in byte data element size (not single precision floating). If you load in the lat lon grid refs as an array just tag each byte onto the array to give 3 elements lat/lon/region.

The new grid box areas have been calculated using the method that Dr Jinlun Zhang has told me he uses. Each grid box has coordinates associated with it, these are available in the grid.dat.pop file. The grid.dat.pop file contains 7 tables of 43200 elements (120x360 = 43200), these are Ulat, Ulon, HTN, HTE, HUS, HUW, and Angle. Ulat and Ulon are the coordinates of each grid box. HTN and HTE are the scalar lengths (km) of the northern and eastern edges of each grid box. HUS and HUW are the vector lengths (km) of the northern and eastern edges of each grid box. Angle is the difference in angle between the latitude line and the grid cell x coordinate line.

In read_hi_uice.f it is stated that "HTN*HTE is the area of a scaler grid cell in km^2 and can be used to calculate sea ice volume and volumes of other variables" This however gives a significant error between the PIOMAS monthly volume series and volume calculated using HTNxHTE, this error is reduced and most of the seasonal variation suppressed by using:

Grid Box Area = Average(HTN,HUS) x Average(HTE,HUW)

This was worked out by Wipneus back in 2011 and I've lived with the -0.6% error since then as 'good enough' for my purposes. I recently emailed Dr Zhang to ask for advice about this, having worked out the regions I thought it best to sort out the grid box areas while I was at it. The answer was quite subtle, I doubt if I would have spotted it, although the clue is in Dr Zhang's comments in his code. The problem is that HTN and HTE are scalar lengths, while HUS and HUW are vector lengths, so we'd been mixing apples and oranges for all that time.

The 'Zhang method' uses HTN and HTE (north and east edge lengths), and to work out HTS and HTW (south and west edge lengths) one simply needs to refer to adjacent cells to calculate HTS and HTW. Recalculating the grid box areas using this method, and comparing volume calculated with the PIOMAS monthly volume gives the error series in green labelled 'Zhang Method'.

Using PIOMAS V2.1: Comparing the volume calculated for the whole PIOMAS domain with the PIOMAS monthly volume series are shown below.

Average error: 4.74ppm
Standard deviation of error: 71.14ppm
Max (Min) error: 216ppm (151ppm)

The Data.

Data area available here.

For ease of most users I have calculated data and release it as CSV files, they're not pretty but handling in code or into any spreadsheet is straightforward. The regional volumes are estimated to be accurate to within about +/-4%, for context the PIOMAS uncertainty (Schweiger et al 2011) ranges from +/-7% in October 1979 to +/-26% in October 2012. This data is provided as is, as the data I've been using. Others are free to use the source gridded data to produce improved regional breakdowns, that is available here.

There are three datasets, all figures are in km^3:

  1. Regional Volume V2.1. Volume calculation derived from PIOMAS gridded thickness, using the Zhang Method calculation of grid box areas (Thanks again Dr Zhang). Volume is broken down into the 15 regions stated below. 
  2. Regional Thickness V2.1, Thickness calculation derived from PIOMAS gridded thickness, Zhang Method area calculation and sea ice concentration from the PIOMAS data. Again this is broken down into the 15 regions stated below. 
  3. Regional Volume Breakdowns V2.1. Volume broken down into contributions from various thickness bands of ice, 10cm thickness bands, 15 regions, with region 16 'All PIOMAS domain' tagged onto the end. No Longer Updated.
  4. Daily Regional Volume Breakdowns V2.1. Volume calculation derived from PIOMAS daily gridded thickness, using the Zhang Method calculation of grid box areas. Volume is broken down into the 15 regions stated below. Current time period 2010 to 2013. Includes listing of error from the main daily PIOMAS series in the final column. No Longer Updated.
The regions used are:

0 Non Regional Ocean
1 Sea of Okhotsk
2 Bering Sea
3 Beaufort Sea,
4 Chukchi Sea
5 East Siberian Sea
6 Laptev Sea
7 Kara Sea
8 Barents Sea
9 Greenland Sea
10 Central Arctic
11 Canadian Arctic Archipelago
12 Baffin Bay/Newfoundland Sea
13 Hudson Bay
14 Gulf Of St Lawrence
15 Land

The regions can be seen on the regional section of the Cryosphere Today site. Regions 14 and 15 have no sea ice, 15 is obvious why (land), 14 is not represented in the PIOMAS domain because it would be a body of water not connected to the bulk of ocean in the model. However they are included for completeness in the CSV files. Thanks to Michael Yorke for improving on my original region mapping from NSIDC to PIOMAS grid, the effect is generally small, but at some months when ice volume in certain regions is low was found to be large in terms of percentage of total volume for those regions. So Michael's hard work to recalculate has been worthwhile. The above listed regional data has been recalculated from 1978 to present to reflect this change.

To help those wanting to access the binary data themselves I have also uploaded four binary masks, 43200 elements, which mirror the PIOMAS gridded file format.

  1. GridArea.bin. Zhang Method calculated grid areas for each grid cell.
  2. Lat.bin. Latitude of each grid cell.
  3. Lon.bin. Longitude of each grid cell.
  4. Region.bin. Region mask with a region number (see list above) for each grid cell.

Zhang, Jinlun and D.A. Rothrock: Modeling global sea ice with a thickness and enthalpy distribution model in generalized curvilinear coordinates, Mon. Wea. Rev. 131(5), 681-697, 2003.


Anonymous said...

Wow, that's dedication. Thanks, Chris. I look forward to seeing what smarter people than I can show from it.

Have a good Christmas break!


Chris Reynolds said...

Thanks Simon,

I'm not breaking just yet, a customer has cancelled and I've got a long weekend coming up. Expect something interesting this weekend. :)

Anonymous said...

Chris, in your latest blog post


you write that you updated the PIOMAS regional data, and you refer to the csv-files on the above web page. However it seems these csv-files were last updated on December 3, and the most recent data in the files are for May 2013?


Chris Reynolds said...

Hi Steven,

Sorry about that, they were showing as updated on my system, but you were right - when I downloaded it was the old data.

Try again using the single link in the (now largely re-written) post. I've linked to the folder instead of the individual files in the hope this will avoid the problem you encountered.

Could you let me know if it works for you?

Anonymous said...

Thanks Chris, it works fine now. It is very interesting.


Chris Reynolds said...

Thanks Steve,

Hope it's of use.

cesium62 said...

I grabbed your regional volume data and made a graph for most of the regions to go along with your central arctic graph of April volumes and summer losses. If you don't already have the graphs lying around, maybe I can save you some typing: https://docs.google.com/spreadsheets/d/1CrSPDI9MhD2pNpzbaKnJvJjpyCGLGToBPvv9NQbGLro/edit?usp=sharing
But you probably have the graphs, and much better organized than I do. So this is just to let you know that I made use of the data you're providing. Thanks.

cesium62 said...

A better link to just the graphs...

Chris Reynolds said...

Thanks Cesium,

I've seen them for all regions but don't have a collection. That's vary useful. I think it would be a good idea to update for every region when I get the September gridded data in early October.

Is all that done in Google Docs? It looks very good.